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Download Paper Quantifying the response of a synthetic light curve generation model to varying inputs. Laurence D. J. Blacketer1, Prof. Hugh G. Lewis1, and Dr. Hodei Urrutxua2 1 Astronautics Research Group, The University of Southampton, Southampton SO17 1BJ, UK 2 Universidad Rey Juan Carlos, Calle Tulipan,´ s/n, 28933 Mostoles,´ Madrid, Spain August 28, 2018 Abstract Ensuring that operating within the near-Earth space environment does not become hampered by increasing num- bers of Resident Space Objects (RSOs) is an important focus for the global space industry. Following research indicating a self-sustaining population of RSOs between 900 - 1000 km driven by collision activity, Active Debris Removal (ADR), the targeted removal of a RSO, was proposed as a possible reactive countermeasure. All of the most viable ADR proposals require accurate characterisation of the target object’s motion both for target selection and for the removal manoeuvre. Another way of safeguarding near-Earth space is through improving upon current Space Situational Awareness (SSA) capabilities. Through better and more accurate positioning, a level of traffic control can be applied to space environ- ment. This would allow for unwanted events to be identified in advance, and responded to more proactively. In either case, new techniques need to be developed for deriving information on object motion, from observation data. The attitude state of the object is of particular interest to both SSA and ADR. For SSA, the attitude of the object has a significant effect on the drag force, which is by far the largest force exerted on objects in Low Earth Orbit (LEO). As for ADR, the majority of proposals require a physical interface with the target object and as a result will rely heavily on attitude state characterisation. Of the available techniques for remote observation and measurement of space objects, optical measurements are by far the cheapest and simplest. As a result, large quantities of time-varying brightness data, on a range of active, in- active and unknown objects, has been collected. Hence developing techniques to derive information, such as attitude state, from light curves could be highly beneficial to ADR and SSA efforts. To examine the availability of attitude information in optical light curve data, a Synthetic Light Curve Forward Model (SLCFM) has been developed. The model uses positional data acquired from the Two Line Element (TLE) database and the Jet Propulsion Laboratory (JPL) HORIZONS database. Brightness is simulated through application of a Cook-Torrence Bidirectional Distribution Reflectance Function (BDRF) to a faceted object geometry. The model inputs are therefore an object geometry, attitude state and the BDRF parameters that define the reflection properties of the surface. This paper quantifies the response of the SLCFM to changes in the inputs by measuring a distance in Hilbert space, using the Chebyshev basis. The synthetic light curves were found to be sensitive to attitude state. It was also found that incorrectly modelling the object geometry and surface optical characteristics can result in significant differences in the resultant light curve. 1 Introduction With the large numbers of Resident Space Objects (RSOs) within the near-Earth space environment, the development of Space Situational Awareness (SSA) techniques and technologies have become a focus throughout the global space sector. One objective of an SSA program is to minimise the risk of operation in space through improving positioning Copyright © 2018 Advanced Maui Optical and Space Surveillance Technologies Conference (AMOS) – www.amostech.com and tracking capabilities. An additional application is in the implementation of a space traffic management system. The aim of such a system would be to exert some level of traffic control over the near-Earth space environment in order to further reduce the possibility of unwanted interactions between RSOs. A further point of consideration is Active Debris Removal (ADR), the targeted removal of an RSO. ADR has been pre- sented as a possible solution to a predicted collision-activity-driven growth in the number of debris fragments between 900 and 1000 kilometres, even in the absence of future launch activity [8], [9]. First identified by debris modelling carried out by the National Aeronautics and Space Administration (NASA), it was subsequently observed using other debris modelling tools, such as the University of Southampton’s Debris Analysis and Monitoring Architecture for the Geosynchronous Environment (DAMAGE) [7]. Although the uncertainties in long term future debris modelling are high, removing objects from space may be a valuable tool for ensuring the sustainability of the near-Earth space environment, and so research and technology demonstration missions are ongoing in this area. One of the most crucial phases of an ADR mission is interfacing with the object. A number of solutions are being researched including robotic arms, harpoons and nets. In any case, accurate attitude determination will be required for selection of suitable targets, and also for carrying out the mission itself. Other fields, such as on-orbit servicing and research into attitude-dependent effects such as drag and solar radiation pressure, could also benefit from these techniques. The largest force experienced by objects in near-Earth orbits is atmospheric drag, which is highly dependent on the object orientation. With a known attitude state this force could be modelled much more accurately, potentially improv- ing predictions of the object’s future position. Attitude state could therefore be highly beneficial for SSA applications. However, because the vast majority of RSOs are uncooperative, the attitude determination must rely on observation data alone. A range of sensors are employed for measurements of space objects. Although highly powerful radar and opti- cal installations are capable of generating accurate measurements, their low number and high cost preclude them from more general application to the RSO population. Alternatively large numbers of small, automated, optical telescopes have been deployed across the globe. One example is the Mini-MegaTORTORA (MMT) system oper- ated by Kazan Federal University, which maintains a publicly accessible catalogue of light curve data, available at astroguard.ru/satellites [1]. As a result, large volumes of optical light curves, which have heritage in attitude and shape detection of Near-Earth Objects (NEOs) such as asteroids [3], [10], [5], have been collected on a wide range of different space objects. Hence optical light curves could potentially form an integral component of a future SSA infrastructure. To explore the attitude detection capability of optical light curves, a synthetic light curve forward model (SLCFM) has been developed. Previous research has examined forward modelling of light curve data and found the results to be highly dependent on the accuracy of the light curve model [12]. The observability of attitude in a single light curve has been examined analytically using the Fisher information matrix. These results found small attitude perturbations to be undetectable in a single light curve. However it is proposed that modelling the object dynamics across a series of measurements could increase the attitude observability [4]. On this basis, and to form a foundation for future work into attitude determination, this paper quantifies the response of the SLCFM to the various inputs and identifies the key sensitivities. 2 Methodology The SLCFM was developed with an objective of simulating real light curve data. This generated a requirement for ephemerides of the Sun, Earth and the object. The NASA Jet Propulsion Laboratory (JPL) HORIZONS database provides the celestial positions and the object position is acquired using Two Line Element (TLE) data together with the Simple General Perturbations 4 (SGP4) propagator. The synthetic light curve is generated through application of a Bidirectional Distribution Reflectance Function (BDRF) to a faceted geometry of the object. The Cook-Torrence model was selected in order to handle the specular component of reflection. This has been shown to be useful for deriving information on attitude state, such as rotation period and Copyright © 2018 Advanced Maui Optical and Space Surveillance Technologies Conference (AMOS) – www.amostech.com Figure 1: Illumination Geometry [2]. rotation axis [2], [6]. Fig. 1 shows the reflection geometry and labels the illumination vector, L, the observation vector V , the angular bisector of these two vectors, H and the two angles a and q. Representing some shape using a faceted geometry allows the apparent magnitude of a collection of Nf acets facets to be given by the sum: Nf acets ! Bi m = −26:74 − 2:5 log10 ∑ 2 (1) i=1 4pr th where −26:74 is the apparent magnitude of the Sun, Bi is the ratio of incident to reflected flux at the i facet, and r is the distance between the surface and the observer. The Cook-Torrence BDRF is then used to calculate a value for Bi, using the equation: Bi = (sRs + dRd)pAi(N i · L)(N i ·V ) (2) th where Rs and Rd are the specular and diffuse bidirectional reflectances, Ai is the i facet area, and s and d are the specular and diffuse coefficients, where s + d = 1. The two bidirectional reflectances are given by: w R = (3) d p where w is the diffuse albedo of the surface, and: F DG Rs = (4) p (N · L)(N ·V ) where F is the Fresnel term, G is the geometric attenuation factor and D is the facet slope function. The geometric attenuation factor is calculated from: 2(N · H)(N ·V ) 2(N · H)(N · L) G = min 1; ; (5) (V · H) (V · H) using the angular bisector, H, calculated from: V + L H = (6) length(V + L) The facet slope function is calculated using the Beckmann distribution: Copyright © 2018 Advanced Maui Optical and Space Surveillance Technologies Conference (AMOS) – www.amostech.com 1 2 D = exp−[tan(a)=m] (7) m2 cos4(a) where m, is the Root Mean Square (RMS) slope defining surface roughness and a is the angle between the angular bisector and the facet normal.
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